Modeling single neuron behavior using stochastic differential equations

Abstract

We model the intrinsic dynamic behavior of a neuron using stochastic differential equations and Brownian motion. Basis of our work is the deterministic one-compartmental multi-conductance model of cerebellar granule cell. We develop a novel modeling approach for our test neuron by incorporating the stochasticity inherently present in the operation of voltage-dependent ion channels. Our new stochastic Hodgkin–Huxley type of model is able to reproduce a large range of dynamics more realistically than previous deterministic models for the granule cell. Proper inclusion of stochastic elements is therefore essential in modeling the behavior of single small neuron.